LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sdrvsp.f
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1 *> \brief \b SDRVSP
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13 * NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NOUT, NRHS
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> SDRVSP tests the driver routines SSPSV and -SVX.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NN
48 *> \verbatim
49 *> NN is INTEGER
50 *> The number of values of N contained in the vector NVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] NVAL
54 *> \verbatim
55 *> NVAL is INTEGER array, dimension (NN)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NRHS
60 *> \verbatim
61 *> NRHS is INTEGER
62 *> The number of right hand side vectors to be generated for
63 *> each linear system.
64 *> \endverbatim
65 *>
66 *> \param[in] THRESH
67 *> \verbatim
68 *> THRESH is REAL
69 *> The threshold value for the test ratios. A result is
70 *> included in the output file if RESULT >= THRESH. To have
71 *> every test ratio printed, use THRESH = 0.
72 *> \endverbatim
73 *>
74 *> \param[in] TSTERR
75 *> \verbatim
76 *> TSTERR is LOGICAL
77 *> Flag that indicates whether error exits are to be tested.
78 *> \endverbatim
79 *>
80 *> \param[in] NMAX
81 *> \verbatim
82 *> NMAX is INTEGER
83 *> The maximum value permitted for N, used in dimensioning the
84 *> work arrays.
85 *> \endverbatim
86 *>
87 *> \param[out] A
88 *> \verbatim
89 *> A is REAL array, dimension
90 *> (NMAX*(NMAX+1)/2)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is REAL array, dimension
96 *> (NMAX*(NMAX+1)/2)
97 *> \endverbatim
98 *>
99 *> \param[out] AINV
100 *> \verbatim
101 *> AINV is REAL array, dimension
102 *> (NMAX*(NMAX+1)/2)
103 *> \endverbatim
104 *>
105 *> \param[out] B
106 *> \verbatim
107 *> B is REAL array, dimension (NMAX*NRHS)
108 *> \endverbatim
109 *>
110 *> \param[out] X
111 *> \verbatim
112 *> X is REAL array, dimension (NMAX*NRHS)
113 *> \endverbatim
114 *>
115 *> \param[out] XACT
116 *> \verbatim
117 *> XACT is REAL array, dimension (NMAX*NRHS)
118 *> \endverbatim
119 *>
120 *> \param[out] WORK
121 *> \verbatim
122 *> WORK is REAL array, dimension
123 *> (NMAX*max(2,NRHS))
124 *> \endverbatim
125 *>
126 *> \param[out] RWORK
127 *> \verbatim
128 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
129 *> \endverbatim
130 *>
131 *> \param[out] IWORK
132 *> \verbatim
133 *> IWORK is INTEGER array, dimension (2*NMAX)
134 *> \endverbatim
135 *>
136 *> \param[in] NOUT
137 *> \verbatim
138 *> NOUT is INTEGER
139 *> The unit number for output.
140 *> \endverbatim
141 *
142 * Authors:
143 * ========
144 *
145 *> \author Univ. of Tennessee
146 *> \author Univ. of California Berkeley
147 *> \author Univ. of Colorado Denver
148 *> \author NAG Ltd.
149 *
150 *> \ingroup single_lin
151 *
152 * =====================================================================
153  SUBROUTINE sdrvsp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
154  $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
155  $ NOUT )
156 *
157 * -- LAPACK test routine --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 *
161 * .. Scalar Arguments ..
162  LOGICAL TSTERR
163  INTEGER NMAX, NN, NOUT, NRHS
164  REAL THRESH
165 * ..
166 * .. Array Arguments ..
167  LOGICAL DOTYPE( * )
168  INTEGER IWORK( * ), NVAL( * )
169  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
170  $ rwork( * ), work( * ), x( * ), xact( * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  REAL ONE, ZERO
177  PARAMETER ( ONE = 1.0e+0, zero = 0.0e+0 )
178  INTEGER NTYPES, NTESTS
179  parameter( ntypes = 10, ntests = 6 )
180  INTEGER NFACT
181  parameter( nfact = 2 )
182 * ..
183 * .. Local Scalars ..
184  LOGICAL ZEROT
185  CHARACTER DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
186  CHARACTER*3 PATH
187  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
188  $ izero, j, k, k1, kl, ku, lda, lwork, mode, n,
189  $ nerrs, nfail, nimat, npp, nrun, nt
190  REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
191 * ..
192 * .. Local Arrays ..
193  CHARACTER FACTS( NFACT )
194  INTEGER ISEED( 4 ), ISEEDY( 4 )
195  REAL RESULT( NTESTS )
196 * ..
197 * .. External Functions ..
198  REAL SGET06, SLANSP
199  EXTERNAL SGET06, SLANSP
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL aladhd, alaerh, alasvm, scopy, serrvx, sget04,
205 * ..
206 * .. Scalars in Common ..
207  LOGICAL LERR, OK
208  CHARACTER*32 SRNAMT
209  INTEGER INFOT, NUNIT
210 * ..
211 * .. Common blocks ..
212  COMMON / infoc / infot, nunit, ok, lerr
213  COMMON / srnamc / srnamt
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max, min
217 * ..
218 * .. Data statements ..
219  DATA iseedy / 1988, 1989, 1990, 1991 /
220  DATA facts / 'F', 'N' /
221 * ..
222 * .. Executable Statements ..
223 *
224 * Initialize constants and the random number seed.
225 *
226  path( 1: 1 ) = 'Single precision'
227  path( 2: 3 ) = 'SP'
228  nrun = 0
229  nfail = 0
230  nerrs = 0
231  DO 10 i = 1, 4
232  iseed( i ) = iseedy( i )
233  10 CONTINUE
234  lwork = max( 2*nmax, nmax*nrhs )
235 *
236 * Test the error exits
237 *
238  IF( tsterr )
239  $ CALL serrvx( path, nout )
240  infot = 0
241 *
242 * Do for each value of N in NVAL
243 *
244  DO 180 in = 1, nn
245  n = nval( in )
246  lda = max( n, 1 )
247  npp = n*( n+1 ) / 2
248  xtype = 'N'
249  nimat = ntypes
250  IF( n.LE.0 )
251  $ nimat = 1
252 *
253  DO 170 imat = 1, nimat
254 *
255 * Do the tests only if DOTYPE( IMAT ) is true.
256 *
257  IF( .NOT.dotype( imat ) )
258  $ GO TO 170
259 *
260 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
261 *
262  zerot = imat.GE.3 .AND. imat.LE.6
263  IF( zerot .AND. n.LT.imat-2 )
264  $ GO TO 170
265 *
266 * Do first for UPLO = 'U', then for UPLO = 'L'
267 *
268  DO 160 iuplo = 1, 2
269  IF( iuplo.EQ.1 ) THEN
270  uplo = 'U'
271  packit = 'C'
272  ELSE
273  uplo = 'L'
274  packit = 'R'
275  END IF
276 *
277 * Set up parameters with SLATB4 and generate a test matrix
278 * with SLATMS.
279 *
280  CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
281  $ cndnum, dist )
282 *
283  srnamt = 'SLATMS'
284  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
285  $ cndnum, anorm, kl, ku, packit, a, lda, work,
286  $ info )
287 *
288 * Check error code from SLATMS.
289 *
290  IF( info.NE.0 ) THEN
291  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
292  $ -1, -1, imat, nfail, nerrs, nout )
293  GO TO 160
294  END IF
295 *
296 * For types 3-6, zero one or more rows and columns of the
297 * matrix to test that INFO is returned correctly.
298 *
299  IF( zerot ) THEN
300  IF( imat.EQ.3 ) THEN
301  izero = 1
302  ELSE IF( imat.EQ.4 ) THEN
303  izero = n
304  ELSE
305  izero = n / 2 + 1
306  END IF
307 *
308  IF( imat.LT.6 ) THEN
309 *
310 * Set row and column IZERO to zero.
311 *
312  IF( iuplo.EQ.1 ) THEN
313  ioff = ( izero-1 )*izero / 2
314  DO 20 i = 1, izero - 1
315  a( ioff+i ) = zero
316  20 CONTINUE
317  ioff = ioff + izero
318  DO 30 i = izero, n
319  a( ioff ) = zero
320  ioff = ioff + i
321  30 CONTINUE
322  ELSE
323  ioff = izero
324  DO 40 i = 1, izero - 1
325  a( ioff ) = zero
326  ioff = ioff + n - i
327  40 CONTINUE
328  ioff = ioff - izero
329  DO 50 i = izero, n
330  a( ioff+i ) = zero
331  50 CONTINUE
332  END IF
333  ELSE
334  ioff = 0
335  IF( iuplo.EQ.1 ) THEN
336 *
337 * Set the first IZERO rows and columns to zero.
338 *
339  DO 70 j = 1, n
340  i2 = min( j, izero )
341  DO 60 i = 1, i2
342  a( ioff+i ) = zero
343  60 CONTINUE
344  ioff = ioff + j
345  70 CONTINUE
346  ELSE
347 *
348 * Set the last IZERO rows and columns to zero.
349 *
350  DO 90 j = 1, n
351  i1 = max( j, izero )
352  DO 80 i = i1, n
353  a( ioff+i ) = zero
354  80 CONTINUE
355  ioff = ioff + n - j
356  90 CONTINUE
357  END IF
358  END IF
359  ELSE
360  izero = 0
361  END IF
362 *
363  DO 150 ifact = 1, nfact
364 *
365 * Do first for FACT = 'F', then for other values.
366 *
367  fact = facts( ifact )
368 *
369 * Compute the condition number for comparison with
370 * the value returned by SSPSVX.
371 *
372  IF( zerot ) THEN
373  IF( ifact.EQ.1 )
374  $ GO TO 150
375  rcondc = zero
376 *
377  ELSE IF( ifact.EQ.1 ) THEN
378 *
379 * Compute the 1-norm of A.
380 *
381  anorm = slansp( '1', uplo, n, a, rwork )
382 *
383 * Factor the matrix A.
384 *
385  CALL scopy( npp, a, 1, afac, 1 )
386  CALL ssptrf( uplo, n, afac, iwork, info )
387 *
388 * Compute inv(A) and take its norm.
389 *
390  CALL scopy( npp, afac, 1, ainv, 1 )
391  CALL ssptri( uplo, n, ainv, iwork, work, info )
392  ainvnm = slansp( '1', uplo, n, ainv, rwork )
393 *
394 * Compute the 1-norm condition number of A.
395 *
396  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
397  rcondc = one
398  ELSE
399  rcondc = ( one / anorm ) / ainvnm
400  END IF
401  END IF
402 *
403 * Form an exact solution and set the right hand side.
404 *
405  srnamt = 'SLARHS'
406  CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
407  $ nrhs, a, lda, xact, lda, b, lda, iseed,
408  $ info )
409  xtype = 'C'
410 *
411 * --- Test SSPSV ---
412 *
413  IF( ifact.EQ.2 ) THEN
414  CALL scopy( npp, a, 1, afac, 1 )
415  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
416 *
417 * Factor the matrix and solve the system using SSPSV.
418 *
419  srnamt = 'SSPSV '
420  CALL sspsv( uplo, n, nrhs, afac, iwork, x, lda,
421  $ info )
422 *
423 * Adjust the expected value of INFO to account for
424 * pivoting.
425 *
426  k = izero
427  IF( k.GT.0 ) THEN
428  100 CONTINUE
429  IF( iwork( k ).LT.0 ) THEN
430  IF( iwork( k ).NE.-k ) THEN
431  k = -iwork( k )
432  GO TO 100
433  END IF
434  ELSE IF( iwork( k ).NE.k ) THEN
435  k = iwork( k )
436  GO TO 100
437  END IF
438  END IF
439 *
440 * Check error code from SSPSV .
441 *
442  IF( info.NE.k ) THEN
443  CALL alaerh( path, 'SSPSV ', info, k, uplo, n,
444  $ n, -1, -1, nrhs, imat, nfail,
445  $ nerrs, nout )
446  GO TO 120
447  ELSE IF( info.NE.0 ) THEN
448  GO TO 120
449  END IF
450 *
451 * Reconstruct matrix from factors and compute
452 * residual.
453 *
454  CALL sspt01( uplo, n, a, afac, iwork, ainv, lda,
455  $ rwork, result( 1 ) )
456 *
457 * Compute residual of the computed solution.
458 *
459  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
460  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
461  $ rwork, result( 2 ) )
462 *
463 * Check solution from generated exact solution.
464 *
465  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
466  $ result( 3 ) )
467  nt = 3
468 *
469 * Print information about the tests that did not pass
470 * the threshold.
471 *
472  DO 110 k = 1, nt
473  IF( result( k ).GE.thresh ) THEN
474  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
475  $ CALL aladhd( nout, path )
476  WRITE( nout, fmt = 9999 )'SSPSV ', uplo, n,
477  $ imat, k, result( k )
478  nfail = nfail + 1
479  END IF
480  110 CONTINUE
481  nrun = nrun + nt
482  120 CONTINUE
483  END IF
484 *
485 * --- Test SSPSVX ---
486 *
487  IF( ifact.EQ.2 .AND. npp.GT.0 )
488  $ CALL slaset( 'Full', npp, 1, zero, zero, afac,
489  $ npp )
490  CALL slaset( 'Full', n, nrhs, zero, zero, x, lda )
491 *
492 * Solve the system and compute the condition number and
493 * error bounds using SSPSVX.
494 *
495  srnamt = 'SSPSVX'
496  CALL sspsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
497  $ lda, x, lda, rcond, rwork,
498  $ rwork( nrhs+1 ), work, iwork( n+1 ),
499  $ info )
500 *
501 * Adjust the expected value of INFO to account for
502 * pivoting.
503 *
504  k = izero
505  IF( k.GT.0 ) THEN
506  130 CONTINUE
507  IF( iwork( k ).LT.0 ) THEN
508  IF( iwork( k ).NE.-k ) THEN
509  k = -iwork( k )
510  GO TO 130
511  END IF
512  ELSE IF( iwork( k ).NE.k ) THEN
513  k = iwork( k )
514  GO TO 130
515  END IF
516  END IF
517 *
518 * Check the error code from SSPSVX.
519 *
520  IF( info.NE.k ) THEN
521  CALL alaerh( path, 'SSPSVX', info, k, fact // uplo,
522  $ n, n, -1, -1, nrhs, imat, nfail,
523  $ nerrs, nout )
524  GO TO 150
525  END IF
526 *
527  IF( info.EQ.0 ) THEN
528  IF( ifact.GE.2 ) THEN
529 *
530 * Reconstruct matrix from factors and compute
531 * residual.
532 *
533  CALL sspt01( uplo, n, a, afac, iwork, ainv, lda,
534  $ rwork( 2*nrhs+1 ), result( 1 ) )
535  k1 = 1
536  ELSE
537  k1 = 2
538  END IF
539 *
540 * Compute residual of the computed solution.
541 *
542  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
543  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
544  $ rwork( 2*nrhs+1 ), result( 2 ) )
545 *
546 * Check solution from generated exact solution.
547 *
548  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
549  $ result( 3 ) )
550 *
551 * Check the error bounds from iterative refinement.
552 *
553  CALL sppt05( uplo, n, nrhs, a, b, lda, x, lda,
554  $ xact, lda, rwork, rwork( nrhs+1 ),
555  $ result( 4 ) )
556  ELSE
557  k1 = 6
558  END IF
559 *
560 * Compare RCOND from SSPSVX with the computed value
561 * in RCONDC.
562 *
563  result( 6 ) = sget06( rcond, rcondc )
564 *
565 * Print information about the tests that did not pass
566 * the threshold.
567 *
568  DO 140 k = k1, 6
569  IF( result( k ).GE.thresh ) THEN
570  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
571  $ CALL aladhd( nout, path )
572  WRITE( nout, fmt = 9998 )'SSPSVX', fact, uplo,
573  $ n, imat, k, result( k )
574  nfail = nfail + 1
575  END IF
576  140 CONTINUE
577  nrun = nrun + 7 - k1
578 *
579  150 CONTINUE
580 *
581  160 CONTINUE
582  170 CONTINUE
583  180 CONTINUE
584 *
585 * Print a summary of the results.
586 *
587  CALL alasvm( path, nout, nfail, nrun, nerrs )
588 *
589  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
590  $ ', test ', i2, ', ratio =', g12.5 )
591  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
592  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
593  RETURN
594 *
595 * End of SDRVSP
596 *
597  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:90
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine ssptrf(UPLO, N, AP, IPIV, INFO)
SSPTRF
Definition: ssptrf.f:157
subroutine ssptri(UPLO, N, AP, IPIV, WORK, INFO)
SSPTRI
Definition: ssptri.f:109
subroutine sspsvx(FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO)
SSPSVX computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: sspsvx.f:276
subroutine sspsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: sspsv.f:162
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:205
subroutine sdrvsp(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SDRVSP
Definition: sdrvsp.f:156
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:120
subroutine sppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPPT05
Definition: sppt05.f:156
subroutine sspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
SSPT01
Definition: sspt01.f:110
subroutine serrvx(PATH, NUNIT)
SERRVX
Definition: serrvx.f:55
subroutine sppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
SPPT02
Definition: sppt02.f:122
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:102